Kirkland was injured in training last week and missed Leicester's 1-0 win over Nottingham Forest and now has returned to parent club Wigan Athletic for treatment of a back injury.
Speaking to the Leicester Mercury, Erikkson said: "Kirkland has gone back to Wigan and we will see when he is fit again if we are doing what kind of deal we are going to do. "First of all he has to get fit so he can start training again. We will see when he can play in December, hopefully. If not, it is unfortunate.
"He has a back problem - spasms. But we don't know when he can start to train again, not even Wigan or himself know that. So that is the problem. It is not the diagnosis because we know what it is. We have to see how he feels day to day. I spoke to him on Friday and he feels much better but he is not ready.
"We have him until the start of January so we have five games to go. But I don't know, we will see when he can start training. He will need at least one week's training before he can play again."